Bayesian and Non-Bayesian Tests of Independence in Seemingly Unrelated Regressions

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Bayesian and non-Bayesian statistics are derived for testing whether or not two blocks of seemingly unrelated regressions are independent. The non-Bayesian statistics are the likelihood ratio test (LRT), Wald's test (WT), and the Lagrange multiplier test (LMT). The authors interpret the LMT and WT as differences in the log of likelihoods conditioned on estimates of nuisance parameters. The Bayesian test is a highest posterior density region test that can also be derived as a Bayes factor. The four tests are compared in sampling experiments. Copyright 1988 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.

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